Pajek Chase Christopherson, Heriberto Diaz, Jiyuan Guo
Pajek overview ● Pajek is designed to be used for analyzing large networks. ● Pajek intends to draw from several sources of machine-readable networks. ● Pajek is free for download online, but is not open source. ● Pajek XXL and Pajek 3XL are alternate versions designed for larger data sets, in the millions of nodes. ● Although it is designed to be used on windows, the Pajek home page contains guides to get Pajek running on MAC and Linux systems using third party software like XQuarts and Wine.
Key Features of Pajek ● Pajek works with six data types: networks, partitions, vectors, permutations, clusters, and hierarchies. ● It is capable of filtering out certain nodes or edges, based on various criteria. ● Large sets of nodes can be grouped together based on a partition, to increase readability of large data sets. ● Already implemented tools to calculate data for each node, exported as a vector: ○ Betweenness Centrality ○ Authorities and Hubs
Advantages of Pajek ● Pajek is up to date, the last update was on January 4th. ● A large amount of documentation is available for Pajek including textbooks for network analysis, based on Pajek, that are geared towards novice users. ● Pajek is a free network analysis software package. ● As you work with a network in Pajek, every intermediary network is saved in a history and can be referred back to. ● Programming knowledge is not required; all key operations are performed through the navigation of the GUI, not from entering scripts. ● One can write macros for Pajek to make it faster to use. ● Information for Pajek is available in several different languages.
Disadvantages of Pajek ● Pajek is primarily for data manipulation, not visualization, so compared to other network analysis software, its ability to generate graphics can be limited. ● Because Pajek is not open source, and is operated through the GUI, it is difficult to extend its functionality. ● In addition to not being open source, even basic documentation about how Pajek’s algorithms are formulated is not available. ● Pajek does not have any versions that are designed for MAC or Linux.
Entering data ● Pajek allows you to describe a network with an input file in three ways ○ By specifying each directed or undirected edge ○ By specifying the directed or undirected edges at each vertex ○ In a matrix format ● Alternatively, one can describe a small network within Pajek and edit it in the draw network tool. ● Finally, data can be obtained online in example files found on Pajek’s homepage or elsewhere in UCINET, GEDCOM, or chemical formats.
Simple example .NET input files Edge by edge Neighbors of vertices Matrix notation *Vertices 5 *Vertices 5 *Vertices 5 1 ”a” 1 ”a” box 1 ”a” 2 ”b” 2 ”b” ellipse 2 ”b” 3 ”c” 3 ”x” diamond 3 ”c” 4 ”d” 4 ”y” triangle 4 ”d” 5 ”e” 5 ”e” 5 ”e” *Arcs *Arcslist *Matrix 1 2 1 1 2 4 0 1 0 1 1 1 4 1 2 3 0 0 2 0 0 2 3 2 3 1 4 1 0 0 2 0 3 1 1 4 5 0 0 0 0 1 3 4 2 *Edgeslist 1 0 0 0 0 4 5 1 1 5 *Edges 1 5 1
Neighbors of vertices drawn
Finding “Centers” Among the functions that can be performed on networks in Pajek is finding so called “centers.” This is done using what Pajek calls a “Robbery Algorithm.” Each node is assigned a weight according to its degree, then if two adjacent nodes have different degree, the higher degree node “steals” weight from the lower degree node. This is repeated until all nodes which are not centers have a weight of zero, and the values stabilize between iterations.
Creating diagram using Pajek Example of World trade a. Using partitions to classify nodes b. Using Kamada-Kawai (Force-directed graph drawing algorithms) to analysis graph c. Using Pajek graph tools to help arrange vertex
Using partitions to classify nodes
Using Kamada-Kawai (Force-directed graph drawing algorithms ) to analysis this graph
Using Pajek graph tools to help arrange vertices
Using Pajek to solve problems Example of USAir: a. Select Airlines one step away from Phoenix Sky Harbor Intl and create partition b. Extract subnetwork by using partition c. Classify all airlines by distances d. Find out the shortest pass or max. flow between two Airlines
Select Airports one flight away from Phoenix and create partition
Extract subnetwork by using partition
Classify all airports by distances (number of flights)
Find out the shortest pass between two Airports
Sources ● Batagelj, Vladamir, and Andrej Mrvar. “Pajek: Analysis and Visualization of Large Networks.” Program Package Pajek / PajekXXL , 5.03, Nov. 1996, mrvar.fdv.uni-lj.si/pajek/. ● Batagelj, Vladamir, and Andrej Mrvar. “Programs for Analysis and Visualization of Very Large Networks Reference Manual.” ● Lin, Jun-Lin, and Laksamee Khomnotai. “Improving Fraudster Detection in Online Auctions by Using Neighbor-Driven Attributes.” Entropy , vol. 18, no. 12, 2015, p. 11., doi:10.3390/e18010011. ● Batagelj, Vladamir, and Andrej Mrvar. “Network Data Sets.” Pajek Data Index , vladowiki.fmf.uni-lj.si/doku.php?id=pajek:data:index. ● Telombardi. “Introduction to Pajek (Part 1 of 3)” Online video clip. Youtube. Youtube, 10 September 2011. Web. 20 February 2018. https://www.youtube.com/watch?v=PRrKo0maZ8Y
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